I started studying Design Concepts in Programming Languages by Turbak, Gifford and Sheldon. In the first chapter, they define a language called POSTFIX, similar to a postfix calculator's input language. This one also has a conditional command and a subroutine-like struct. So, it seemed like it could implement a looping construct like while. But later, the book gives proof that POSTFIX is not able to encode infinite loops, programs always terminate.
In an exercise, the book wants me to implement a factorial program in POSTFIX, if possible. I tried and failed miserably for hours. I looked up on primitive recursive functions, which factorial is one. Found a language called LOOP, designed by Uwe Schöning that can compute only the primitive recursive functions. I tried implementing in POSTFIX a looping construct that always terminates but could not do it. Because the language does not have any naming or abstraction facilities, I could not see how I can do it.
What I ask is this:
Using the POSTFIX definition given on the below link, can someone implement a language construct that can be used to implement primitive recursive functions, like implementing a looping construct that always terminates? Or give a proof that it is not possible maybe.
Note: There is a draft of the book (thanks @YuvalFilmus) where you can find the description of POSTFIX language (section 1.4, pp5).